Why does the weight of the water depend on temperature?
Ok - splitting hairs now.
I agree that if you change the temperature of water, its weight will not change - its volume will.
But the question asked how much a gallon of (some liquid) weighs. Measure out a gallon of water at 5 degrees, and weigh it. Then increase the temperature to 25 degrees, and weigh it again. Of course its weight won't have changed (ignoring the effect of evaporation). But it's no longer a gallon - it's now more than a gallon. So yes, if you think about it, a gallon of water at 5 degrees weighs more than a gallon of water at 25 degrees.
FFF
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